Statistics: Experimental Design N Butterworth East River High School Rev 21 August 2016

Designing a Statistical Study: Guidelines. Identify the variable(s) of interest (the focus) and the population of the study. Develop a detailed plan for collecting data. If you use a sample, make sure the sample is representative of the population. Collect the data. Describe the data, using descriptive statistics techniques. Interpret the data and make decisions about the population using inferential statistics. Identify any possible errors.

Data Collection: An Observational Study: Observe and measure the characteristics of interest without changing the existing conditions. An Experiment: A treatment is applied to a part of the population and responses are observed. Another part of the population may be used as a control group, in which no treatment is applied. Subjects (experimental units) can be given a placebo to keep subjects from knowing which group is given a treatment.

Data Collection: A Simulation: Use a mathematical or physical model to reproduce the conditions of a situation or process. Simulations allow you to study situations where collecting data can be impractical or dangerous. A Survey: An investigation of one or more characteristics of a population. The most common types of surveys are completed by interview, mail, or telephone. In an survey it is important to word questions carefully so that they are unlikely to bias the results.

Terms: Confounding Variable: When an experimenter cannot tell the difference between the effects of different factors on a variable. Blinding: A technique where the subjects do not know whether he or she received the treatment or the placebo. Double-blind: A technique where neither the subjects nor the experimenter knows which subjects receive the treatment or the placebo.

Terms: Placebo Effect: When a subject reacts favorably to a placebo when in fact he or she has been given no medical treatment at all. Randomization : The process of randomly assigning subjects to different treatment groups. Replication: The repetition of an experiment using a large group of subjects.

Census vs. Sampling: Census: When results from every subject (experimental unit) is recorded/measured. Random Sampling : The process of randomly assigning subjects to different treatment groups where each subject is equally likely to be chosen.

Sampling Techniques: SRS (Simple Random Sample): A method of choosing experimental units (subjects) where individuals are chosen entirely by chance from the population. Ex: Pulling names out of a hat. Stratified Sampling: A method of choosing experimental units (subjects) where the population is first divided into strata (groups) based on some convenient method of separating subjects, then individuals are chosen from each of the strata. There is no particular expectation of differences in results from each of the strata. Ex: Freshmen, Sophomores, Juniors, Seniors. Blocking: Dividing a population into groups based on an expectation of marked differences in results. The samples are then chosen equally among each block. Ex: Subdividing the population into smokers, former smokers, and non- smokers with an expectation that a health study would show an increase in health issues for some groups. Distributing members of each group across the samples will reduce the differences in the results.

Sampling Techniques: Cluster Sampling: A method of choosing experimental units (subjects) where the population is divided into naturally occurring sub-groups. Each cluster should consist of members with all of the characteristics of the population. Each subgroup is equally likely to be chosen for the sample. Every individual in each subgroup is recorded/measured. Ex: Dividing a crop of bean plants into square feet, numbering each plot. Select every individual in each randomly chosen plot. Systematic Sampling: A method of choosing experimental units (subjects) where you order the population in some convenient manner, then systematically select units. Ex: Every 10th student on the school’s roster. Every 3rd person in the right-hand column of the phone book.